A polynomial equation (e.g., x^3-2x^2-3x=0) can be solved by factoring and using the zero-product rule (e.g., x(x+1)(x-3)=0 gives x=0,-1,3). Knowing how to accurately factor down completely is key! Watch for GCFs and special factoring forms.

Objectives

By the end of this topic you should know and be prepared to be tested on:

7.4.1 Differentiate between "factoring a polynomial expression" and "solving a polynomial equation".

7.4.2 Solve polynomial equation by factoring and using the zero-product rule (This is key!)

7.4.3 Recognize how many solutions a polynomial equation will have by observation of its factored form

7.4.4 Recognize how many zeros a polynomial function has by observation of its graph

It is recommended that you be able to use a calculator (handheld or software) to solve a polynomial equation graphically by electronically finding its x-intercept values. If you have a handheld graphing calculator then these sites may help: